Fluid Phase Equilibria

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1 Fluid Phase Equilibria Contents lists available at ScienceDirect Fluid Phase Equilibria journal homeage: Henry s law constant and related coefficients for aqueous rocarbons, CO 2 and H 2 S over a wide range of temerature and ressure Vladimir Majer a,, Josef Sedlbauer b,, Gaetan Bergin a a Laboratoire de hermodynamique des Solutions et des Polymères, Université Blaise Pascal Clermont-Ferrand/CNRS, Aubière, France b Deartment of Chemistry, echnical University of Liberec, Liberec, Czech Reublic article info abstract Article history: Received 7 Aril 2008 Received in revised form 14 July 2008 Acceted 29 July 2008 Available online 6 August 2008 Keywords: Henry s law constant Aqueous Hydrocarbons CO 2 H 2S his article resents three interrelated toics. First, the Henry s law constant HLC and its use are reviewed in a broader thermodynamic context reaching beyond the restricted image of HLC as a coefficient reflecting artitioning between liquid and vaor hases. he relationshis of HLC to the vaor liquid distribution coefficient and the air water artition coefficient are discussed as well as the interrelation between exressions of HLC in terms of different concentration scales. Second, the reviously ublished grou contribution method for estimation of HLC of rocarbons [J. Sedlbauer, G. Bergin, V. Majer, AIChE J ] is extended by adding the newly determined arameters for CH 4,CO 2 and H 2 S. Inclusion of these three major constituents of the natural gas makes the method more versatile in alication to systems where oil and/or natural gas coexist with an aqueous hase. When establishing the arameters of the model the reresentative HLCs from literature were combined with the data on the derivative roerties available over a wide range of conditions from the calorimetric and volumetric exeriments. An attention is aid articularly to the effect of ressure on the HLC. hird, a convenient user-friendly software ackage is described allowing calculation of HLC and of other related coefficients over a wide range of temerature and ressure on the basis of the resented model. his ackage is available on request in an executable form on a shareware basis for non-commercial users Elsevier B.V. All rights reserved. 1. Introduction he Henry s law constant K H is a quantity frequently alied in the thermodynamic descrition of dilute aqueous solutions. It was originally roosed more than 200 years ago [1] as a measure of gas solubility in a liquid, and exressed as a ratio of the artial ressure of a gaseous solute to its equilibrium concentration in the liquid hase. he ercetion and use of the Henry s law constant today is, however, much broader; from the hysicochemical oint of view K H is basically a coefficient relating the fugacity of a dissolved nonelectrolyte to its concentration in a solution. he solute can be in the ure state gaseous, liquid or solid and solvent is often water. he Henry s law constant is namely used in environmental chemistry and atmosheric hysics as a major criterion for describing air water artitioning of solutes at nearambient conditions. It lays a major role in evaluating the transort of ollutants between atmoshere and aquatic systems, rain water Corresonding author. el.: ; fax: Corresonding author. el.: ; fax: addresses: vladimir.majer@univ-bclermont.fr V. Majer, josef.sedlbauer@tul.cz J. Sedlbauer. and aerosols. he Henry s law constant is also used extensively in chemical engineering and geochemistry for designing or describing rocesses where dilute aqueous systems are involved, often over a wide range of temerature and ressure. In this case it is necessary to adot some theoretically founded concets allowing a realistic calculation of the Henry s law constant at suerambient conditions. he use of the Henry s law constant by different communities is reflected by the establishment of multile and alternative definitions of this quantity, leading to a considerable confusion in literature. hus, the Henry s law constant is certainly a coefficient the most frequently alied in hase equilibrium calculations concerning dilute solutions, but its thermodynamic essence is often misunderstood or misinterreted. For that reason we have found useful to resent in the first art of this aer a concise review of the thermodynamics regarding the Henry s law constant and to show how the different versions of K H and other related coefficients are interconnected. An effort has been made over the ast years to use the QSPR 1 concets for building u linear rediction schemes for the Henry s 1 QSPR quantitative structure roerty relationshi /$ see front matter 2008 Elsevier B.V. All rights reserved. doi: /j.fluid

2 66 V. Majer et al. / Fluid Phase Equilibria law constant, covering a variety of organic solutes in water. After the ioneering work of Hine and Mookerjee [2] this aroach has become namely oular in environmental chemistry where different methods using fragmentary contributions [3], toological descritors [4,5] or solvochromic arameters [6 8] have been used for estimations at 298 K. In addition, more sohisticated, yet mainly emirical, comutational models were introduced recently using quantum mechanical descritors [9 11] and advanced statistical techniques based on neural networks [12 14]. While all these schemes are designed for redictions at near-ambient conditions, the methods for estimation of the Henry s law constant as a function of temerature are limited. Sedlbauer et al. [15] have ublished a model allowing calculation of the Henry s law constant for aqueous C 2 to C 12 rocarbons over a wide range of temerature 273 < < 573 K and ressure 0.1 < < 100 MPa. he grou contribution aroach was used for calculating the arameters of a thermodynamically sound model for infinite dilution roerties [16] allowing to obtain K H via the Gibbs energy of ration. Besides clarifying various concets of the Henry s law constant this article has basically two objectives. First, the reviously ublished estimation method of Sedlbauer and collaborators is extended by adding the arameters for CH 4, CO 2 and H 2 S. Inclusion of these three major constituents of the natural gas encountered frequently in the resence of other rocarbons N C > 2 makes the method more versatile for hase equilibrium calculations in systems where oil and/or natural gas coexist with an aqueous hase. When establishing the arameters for these three gaseous solutes we have combined the reresentative Henry s law constants selected recently by Fernandez-Prini et al. [17] with the data on the derivative roerties available over a wide range of conditions from the calorimetric and volumetric exeriments. An attention is aid articularly to the effect of ressure on the Henry s law constant of gases and liquids. Second, a convenient user-friendly software ackage is described allowing calculation of the Henry s law constant and several related coefficients characterizing vaor liquid equilibria over a wide range of conditions. his ackage is available on request in an executable form on a shareware basis for noncommercial users. Availability of such a software tool is imortant for imlementation of the method. he rerogramming of the model would be comlex, requiring, e.g. the use of the same fundamental EOS for water as that alied when establishing the grou contributions for calculating the arameters of the model. 2. hermodynamic background he aim of the following outline of basic equations is to resent the Henry s law constant in a broader thermodynamic context going beyond its restrictive viewing as a coefficient reflecting artitioning between the liquid and vaor hases, as well as to elucidate the interrelation between the related coefficients defined in terms of different concentration scales. he Henry s law constant K H is defined in modern chemical thermodynamics as the limiting fugacity/molar fraction ratio of a solute in a solution [18,19] and has therefore the dimension of ressure K H [, ] = lim x s 0 fs x s Fugacity of the solute f s and its molar fraction x s relate to the same hase, thus this is a one-hase definition of the Henry s law constant without assumtion of any kind of the hase equilibrium 1 condition. For that reason it is a function of two indeendent variables, temerature and ressure. 2 he chemical otential of a solute in a solution the artial molar Gibbs energy, Ḡ s can be exressed deending on the choice of the standard state G ig s [, ref ] for ideal gas at a reference ressure ref = 0.1 MPa, or Gs [, ] for infinitely dilute solution3 as Ḡ s [, ] = G ig fs s [, ref ] + R ln = Gs [, ] + R lnx ss H 2 ref he symbol s H stands for the dimensionless activity coefficient comatible with the Henry s law, i.e. lim xs 0s H = 1 Combination of Eqs. 1 and 2 in the limit of infinite dilution leads to the exression KH [, ] R ln = Gs [, ] Gig s [, ref ] = G [, ] 3 ref where G is the Gibbs energy of ration corresonding to the transfer of a solute from an ideal gas state to an infinitely dilute solution. For descrition of solutions, other concentration variables are sometimes referred to the molar fraction x s. hese are namely molality m s mol/kg oular with geochemists or molarity c s mol/m 3 used often in environmental science. It holds in the limit of infinite dilution lim m s = x s 0 x s and lim M w x s 0 c s = x s w 4 M w where M w kg/mol and w kg/m 3 are the molar mass and density of water, resectively. he values of the standard state chemical otentials are therefore affected by the choice of the concentration variable as follows Gsm = G sx + R lnm wm o and Gsc = G sx + R ln Mw c o 5 w Since activity coefficients are always dimensionless, the standard concentrations m o = 1 mol/kg and c o = 1 mol/m 3 must be introduced for converting molality and molarity to dimensionless concentration variables. Introduction of Eq. 5 into Eq. 3 then leads to the relationshi between K H and the alternative definitions of the Henry s law constant in terms of molality K Hm and molarity K Hc.It holds: fs K Hm = lim = K Hx M w m o and m s 0 fs c o K Hc = lim = K Hx M w 6 c s 0 c s /c o w his means that both K Hm and K Hc have also dimension of ressure and are thus consistent with Eqs. 3 and 5. In ractical use, the alternative Henry s law constants are, however, usually exressed simly as a ratio of ressure to molality or molarity. While this is not strictly rigorous in the light of the above relationshis, this simlified convention allows to distinguish immediately what concentration scale was selected and is therefore generally used in alications. m s /m o 2 he definition of the Henry s law constant introduced here is of course more general than that resulting from the historical understanding of K H exclusively as a arameter reflecting the gas solubility. When the Henry s law constant is obtained exerimentally from the vaor liquid equilibrium measurements it is related logically to the vaor ressure of the solvent due to the limit of infinite dilution. 3 his standard state adoted for aqueous secies is unit activity in a hyothetical solution of unit concentration referenced to infinite dilution denoted with suerscrit.

3 V. Majer et al. / Fluid Phase Equilibria he derivatives of Eq. 3 allow establishing the exact thermodynamic relationshis describing the temerature and ressure deendence of the Henry s law constant. It holds: R 2 lnkh [ ] R 2 lnk H ln KH = Hs [, ] Hig s [, ref ] = H 7 = C,s [, ] Cig,s[, ref ] = C, 8 R = Vs [, ]. 9 he standard thermodynamic roerties enthaly, heat caacity and volume of solute relate to an ideal gas H ig s,c,s ig oran infinitely dilute solution Hs,C,s,V s. It follows from Eqs. 7 and 8 that the temerature deendence of the Henry s law constant can be calculated by integrating the derivative ration roerties H, C that are accessible from calorimetric and sectroscoic measurements. Enthaly of ration H is calculated as, a combination of heat of solution and the residual enthaly difference between the enthaly of ure solute and that of an ideal gas that is in absolute value close to the enthaly of vaorization for liquid solutes. he heat caacity of ration C,, calculated as a difference of solute heat caacity at infinite dilution and that of an ideal gas, is ositive and increasing with temerature for volatile nonelectrolytes [20]. H values, generally negative at near-ambient conditions, become ositive at high temeratures, scaling with water exansivity and diverging when aroaching the critical oint of water. he Henry s law constant is therefore at first increasing with temerature, exhibiting a maximum tyically between 373 and 473 K, and decreasing with temerature when aroaching the critical oint of water. Similarly the change of the Henry s law constant with ressure can be calculated by integrating Eq. 9 where the artial molar volume at infinite dilution of a solute Vs is accessible from densitometric measurements. Its value is roortional to the molar mass of solute at room temerature and scales with comressibility of water at conditions remote from ambient, diverging ositively at the critical oint of water for volatile nonelectrolytes [20]. he Henry s law constant is therefore generally increasing with increasing ressure. he integral of Eq. 9 between saturation ressure of the solvent and ressure of the system is identical with the Krichevski Kasarnovsky equation used in the chemical engineering literature for calculating the so-called Poynting correction exressing the change of fugacity with ressure. It is aarent from the combination of Eqs. 6 9 that K Hm and K H have identical temerature and ressure sloes while a minor difference is observed in the case of K Hc where the mechanical coefficients of water exansivity and comressibility lay a role. he Henry s law constant is used mainly for the descrition of vaor or gas liquid equilibria and the comositions of coexisting hases y s and x s obtained from exeriments are at the same time also the major data source for determining K H of volatile solutes: y s ϕ s = K H [, sat w ]ex sat w Vs [, ] d R x s H s. 10 he symbols, ϕ s and sat w denote the overall ressure, the fugacity coefficient of a solute in the vaor and the saturation ressure of water, resectively. Since the Henry s law constant is defined in the limit of infinite dilution Eq. 1, it can be obtained from exerimental vaor liquid equilibrium data when sat s. hen in the above relationshi both the exonential term the Poynting correction and s H aroach unity. he temerature deendence of the Henry s law constant is therefore mostly resented in the literature along the saturation line of water and for that reason some authors maintain that K H is a function of one indeendent variable only temerature e.g. [21 23]. his statement is, however, not quite correct considering the direct link of the Henry s law constant with the Gibbs energy of ration and imlying a general validity of Eq. 9. It is in rincile always ossible to construct the thermodynamic surface of K H [, ] with two indeendent state variables. he limited amount of the volumetric data for aqueous solutes, esecially at suerambient conditions, is, however, a major obstacle. Without this information it is difficult to searate in Eq. 10 the effect of ressure on the Henry s law constant from the nonideality of aqueous solution since the concentration of solute x s is increasing due to increasing ressure and the solution cannot then be considered as ideal s H /= 1. his interconnection between the Poynting and nonideality corrections hamers the use of highressure vaor liquid equilibrium data for K H determination [65]. he Henry s law constant of saringly soluble liquids or solids in water is determined from their solubilities xs sol Vs sat sat s ϕs sat ex R s in water as follows: = K H [, ]xs sol 11 where sat s and V s are the vaor ressure and molar volume of ure solute, resectively. his equation is valid for low solubilities where s H 1 and in the cases where the solubility of water in the nonaqueous hase can be neglected. Since the volume of a condensed solute changes little with ressure, this equation is a good aroximation that allows to calculate the Henry s law constant as a function of both temerature and ressure. At low ressures it simly holds that K H = sat s /xs sol, this relationshi being the main avenue used for calculating the Henry s law constant of low volatility solutes that are saringly soluble in water. he symmetrical limiting activity coefficients s R comlying with the Raoult s law lim xs 1s R = 1 are extensively used in engineering thermodynamics for describing nonideality of dilute solutions at temeratures u to 373 K and at ambient ressure. heir determination from the hase equilibrium data is carried out tyically via the Henry s law constant or related coefficients defined below. Since the fugacity of a solute in the liquid hase can be exressed as f s = f l s x ss R, the combination with Eq. 1 gives K H = f l s R s = sat,l s s R 12 where f l s and sat,l s are the fugacity and saturation vaor ressure of a real or hyothetical liquid solute. Several other coefficients closely related to K H were introduced for describing the artitioning of solutes between the vaor and liquid hases. his is the case of the vaor liquid distribution coefficient K d denoted sometimes also as the limiting relative volatility that is defined as K d = lim x s 0 ys x s 13 It follows immediately from Eq. 10 for a binary system consisting of a solute and water K d = K H[, sat w ] sat w ϕw sat 14 where ϕ sat w is the fugacity coefficient of saturated water vaor. It means that K d corresonds simly to the ratio of the Henry s law constant and saturation vaor ressure at conditions where vaor hase nonideality can be neglected. Coefficient K d is logically defined exclusively along the saturation line of solvent. he Henry s law constant is often considered in geochemistry and atmosheric hysics as a thermodynamic reaction constant

4 68 V. Majer et al. / Fluid Phase Equilibria corresonding to a ration rocess where the solute is transferred from an ideal gas state to an ideal aqueous solution with the standard states defined in terms of unit molality or molarity. hus, the following two coefficients K Hm = m s s m o = and K K Hc = c s c o = 15 Hm s K Hc are encountered in literature. he symbol s is the artial ressure of a solute in the vaor hase and the concentration variables exress concentration of the solute in the aqueous hase. he air water artition coefficient K aw characterizing equilibrium distribution of a solute between the atmosheric and aqueous hases is defined as the limiting molarity ratio K aw = lim c w s 0 c a s c w s, 16 where cs a and cw s are the equilibrium concentrations of a solute in air and water, resectively. his coefficient is sometimes called in environmental chemistry the dimensionless Henry s law constant. In the limit of infinite dilution it holds for the aqueous hase cs w = xs w w/m w and the atmosheric hase can be aroximated by an ideal gas equation of state, cs a = a s /R where a s is the artial ressure of solute in the air. Since at atmosheric conditions a s = K Hxs w, it holds K aw = K HM w = K Hm = K Hc 17 R w R w m o Rc o his coefficient K aw is resented tyically at 298 K or over a limited temerature interval at near-ambient conditions. aking into account Eq. 7 it follows for the temerature deendence of K aw : lnkaw ln KH = + w 1 = H /R + w 1 18 where w is water comressibility. At temeratures close to ambient H /R and w are of the order of 10 and 0.1, resectively. hen the above relationshi suggests that the temerature sloe of K aw is about 10% lower comared to that for K H. 3. Descrition of the grou contribution method for K H he Henry s law constants is calculated as a function of temerature and ressure via the Gibbs energy of ration that can be exressed as follows [24] KH R ln = G [, ] = G [ ref, ref ] ref ref S [ ref, ref ] + ref C, ref dln + ref C, ref d ref V s d 19 where G [ ref, ref ] and S [ ref, ref ] are the terms relating to the reference state at ref = and ref = = 0.1 MPa. he entroic term is tyically obtained as H S [ [ ref, ref ] G [ ref, ref ] ref, ref ] = 20 ref using the Gibbs energy and enthaly reference state data. he three integrals exress the change with temerature and ressure, the suerscrits ref and indicate the constant variable at which the integration is erformed. We have adoted an aroach combining two distinct schemes; one for calculating the values of able 1 Grou contributions for calculating G [ ref, ref ] and S [ ref, ref ]; values of grou contributions for rocarbons C 2 and higher are from lit [25]; values for CH 4, CO 2 and H 2S are obtained from the data in lit [17,26] Functional grou G [ ref, ref ] kj mol 1 S [ ref, ref ]Jmol 1 K 1 a Y SS C b CH b CH b CH b C C b c H b c-ch d b c-ch b e C ar b CH ar b IC C f b CH b CO b H 2S b a he standard state term to be used as Y [ N ref, ref ] = Y SS + n iy where i=1 s,i Y are individual grou contributions and n s,i i is the number of their occurrences in the molecule. Standard state term is also used in the case of CH 4,CO 2 and H 2S. b Entroic grou contributions were calculated from Eq. 20. c Hydrogen atom bound to alkene grou. d Prefix c denotes a cycloalkane grou. e Grou with subscrit ar is a art of aromatic ring. f Correction for ortho osition on aromatic ring. G [ ref, ref ] and S [ ref, ref ], and the second for exressing the three integrals in Eq. 19. he Gibbs energy and entroy of ration at the reference state ref, ref are obtained for rocarbons C 2 and higher from the grou contributions for G [ ref, ref ] and S [ ref, ref ] tabulated by Plyasunov and Shock [25]. In the case of CH 4, CO 2 and H 2 S G [ ref, ref ] was calculated from the Henry s law constant at K obtained from the evaluated data by Fernandez-Prini et al. [17] using Eq. 3. he S [ ref, ref ] values are those recommended by Plyasunov et al. [26]. able 1 lists the concrete Gibbs energy and entroy of ration values: the first line contains the intrinsic Y SS values that corresond to the material oint contribution to the Gibbs energy and entroy of ration. his term is derived from statistical mechanics [27] and can be calculated using only the roerties of ure solvent: R G SS = R ln V w GSS R S SS = = R ln + 1 w 21 V w where = 0.1 MPa and V w and w are the molar volume and the coefficient of thermal exansion of water, resectively. he sum of the three integrals on the right-hand side of Eq. 19 is calculated from the high-temerature ration model Sedlbauer O Connell Wood, SOCW roosed by Sedlbauer et al. [16]. Since the integration of the standard heat caacity equation is comlex within this model it is more convenient to rearrange Eq. 19 as follows: G [, ] = G [ ref, ref ] ref S [ ref, ref ] + G mod [, ] G mod [ ref, ref ] ref S mod [ ref, ref ] 22 It is aarent that the sum of integrals is relaced by a combination of three terms denoted by suerscrit mod using the

5 V. Majer et al. / Fluid Phase Equilibria able 2 Grou contributions for calculating arameters of the, deendent SOCW model Functional grou a 10 3 m 3 kg 1 mol b 10 4 m 3 kg 1 mol c 10 6 m 3 kg 1 mol d e 10 J K 2 mol 1 C a CH a a CH a CH C C a a H c-ch a a c-ch a C ar a CH ar b CH b CO H 2S b a Grou contributions for rocarbons reorted by Sedlbauer et al. [15]. b Parameters for individual comounds determined in this work. exressions for the Gibbs energy and entroy of ration from the high-temerature model. he equation for the standard molar volume of an aqueous solute is the basic relationshi of the SOCW model: V s = R w + dv w R w + R w w a + bex[ϑ w ] 1 + c ex [ ] + ıex[ w ] 1 23 where = m 3 /kg, = 1500 K and = 0.01 m 3 /kg are the redetermined general constants valid for all solutes. he solute secific adjustable arameters are a, b, c and d, while ı = 0.35a holds for all nonelectrolytes. his equation is in fact modeling a series of erturbation effects due to: i insertion of a material oint into water solvent V SS =R w, ii growing it to a waterlike molecule with size adjusted to mimic the intrinsic volume of a solute dv w R w, and iii then changing its otential field from solvent solvent to solute solvent interaction. his last contribution is modeled by the third term on the right-hand side of Eq. 23 that is urely emirical. his equation has correct limiting behavior, i.e. it reduces to the virial equation truncated after the second virial coefficient at low densities and diverges at the critical oint of water [16]. Since the rocess of ration is defined as an isothermal transfer of a solute molecule from an ideal gas state at ref =0.1MPa to aqueous solution at a ressure it is ossible to write the Gibbs energy of ration as 0 G mod = R dln + V s ref 0 d + G cor 24 where Vs is exressed from Eq. 23. An additional emirical correction term G cor is needed at subcritical conditions since the simle volumetric Eq. 23 is not sufficient for describing quantitatively the integration across the vaor liquid saturation line. his correction is defined on the heat caacity level and for nonelectrolytes has the form 2 G cor 2 = S cor = C cor, = e c 2 228, < c 25 where e is an additional adjustable arameter. Contribution of the correction term is decreasing with increasing temerature and it vanishes at the critical temerature of solvent G cor = H cor = C cor, = 0, c thus roviding integration constant for Eq. 24. Once the exression for G mod is available, the model equation for the entroy of ration also required in Eq. 22 is simly obtained as S mod = G mod 26 Full exressions for G mod, S mod and other thermodynamic functions within the SOCW model can be found in Aendix A. he five arameters a, b, c, d, e of the temerature and ressure deendent model are obtained for rocarbons N C >1from the grou contributions tabulated in able 2. Each arameter for the solute of interest is calculated as a linear combination of the able 3 Survey of the database of exerimental values Comound tye otal number of exerimental values number of comounds K H H C,s V s Alkanes N C > Alkenes Cycloalkanes Alkylbenzenes Alcohols otal CH CO H 2S

6 70 V. Majer et al. / Fluid Phase Equilibria aroriate arameters of constituting grous, e.g. N a = n i a i 27 i=1 where N is the total number of structural grous resent in the given solute, n i is the number of occurrences of each secific grou, and a i stands for the a arameter of the ith grou taken from able 2. he molecular fragments are defined in an identical way as the grou contributions used for the calculation at the reference conditions ref, ref able 1, the roximity effect IC C on aromatic ring is not, however, considered. he material oint contribution Eq. 21 that is temerature deendent aears exlicitly in Eq. 24 and therefore it is not listed in able 2. he grou contributions for C 2 and higher rocarbons were taken over from the article by Sedlbauer et al. [15]. For illustration able 3 gives the number of data oints and comounds that were considered er class of rocarbons when determining the grou contributions by simultaneous correlation of the exerimental Henry s law constants and their derivative roerties. A certain amount of data on derivative roerties C,,V s for alcohols were also included that was helful for increasing numerical stability of the grou contribution determination for the less frequent functional grous for more information see reference [15]. Using analogous simultaneous correlation rocedure like for rocarbons, the arameters were newly determined for CH 4, CO 2 and H 2 S. hese three aqueous solutes belong to exerimentally well-studied systems with data available for most roerties characterizing ration at elevated temeratures and extending in the case of Vs and C to suercritical conditions. When, establishing the arameters of the SOCW model we have used the Henry s law constants along the saturation line of water determined from the gas solubility data reorted in a variety of literature sources listed in able 4. Major sources of derivative roerties were the aers by Hnedkovsky and Wood [38] and by Hnedkovsky et al. [42], reorting the standard heat caacities obtained by the Picker-tye flow calorimetry and the standard volumes from measurements by vibrating tube densimetry, resectively. hese data were included for the three gases u to 623 K and 35 MPa in the case of volumes and at one isobar 28 MPa for the heat caacities. he enthalies of ration are available for CH 4 at temeratures to 323 K, originating from the unique measurements carried out by the grous of Gill et al. [34,35,37] and Wadsö and co-workers [36]. Only one enthalic data oint at 298 K is, however, reorted for CO 2 and H 2 S. he roerties of the solutes in the ideal gas hase, needed for converting C,s to C, were taken from the JANAF, hermochemical ables [40]. Overall numbers of data oints relating to individual thermodynamic roerties are resented for the three gases in able 3 and a detailed survey is given in able 4. he arameters of the SOCW model were obtained by the simultaneous correlation of the Henry s law constants and the data on the three derivative roerties using the weighted least squares rocedure with weights reflecting the exected exerimental uncertainties. hey were estimated at 2% for K H of CH 4 and at 3% for CO 2 and H 2 S, based on the root-mean-square deviations of the data from the correlation of Fernandez-Prini et al. [17]. For the derivative roerties the exected errors were set between 1% and 3% for H and V s, and between 3% and 5% for C,, according to the error estimates in the original data sources and the fact that the relative error increases with the temerature. he objective minimized function O was defined as O = n 4 j [ j=1 i=1 X mod,j i X ex,j i X j i ] 2 28 able 4 Survey of data sources to determine the arameters of the SOCW model Literature sources in chronological order Pro. N oints K MPa CH 4 Michels et al. [28] K H sat Culberson and McKetta [29] K H sat Sultanov et al. [30] K H sat Rettich et al. [31] K H sat Cramer [32] K H sat Crovetto et al. [33] K H sat Dec and Gill [34] H Dec and Gill [35] H Oloffson et al. [36] H Naghibi et al. [37] H Hnedkovsky and Wood [38] C ieel and Gubbins [39] V Moore et al. [41] V Hnedkovsky et al. [42] V CO 2 Wiebe and Gaddy [43] K H sat Wiebe and Gaddy [44] K H sat Morrison and Billet [45] K H sat Malinin [46] K H sat Ellis and Golding [47] K H sat akenouchi and Kennedy [48] K H sat Murray and Riley [49] K H sat Cramer [32] K H sat Shagiakhmetov and arzimanov K H sat [50] Müller et al. [51] K H sat Nishswander et al. [52] K H sat Crovetto and Wood [53] K H sat Bamberger et al. [54] K H sat Berg and Vanderzee [55] H Barbero et al. [56] C Hnedkovsky and Wood [38] C Moore et al. [41] V Hnedkovsky et al. [42] V H 2S Selleck et al. [57] K H sat Lee and Mather [58] K H sat Gillesie and Wilson [59] K H sat Carroll and Mather [60] K H sat Cox et al. [61] H Barbero et al. [62] C Hnedkovsky and Wood [38] C Barbero et al. [56] V Hnedkovsky et al. [42] V where X j and X j stand for K H, H, C,,V s and their errors, resectively, and n j are the numbers of data oints for the four roerties. Exlicit equations for the thermodynamic functions resulting from the SOCW model denoted with the uer index mod in Eqs are resented in Aendix A. he adjustable arameters of the SOCW model obtained for aqueous CH 4,CO 2 and H 2 S are summarized in able 2 along with arameters for the rocarbon functional grous evaluated earlier [15]. A quantitative comarison is made in able 5 between the data calculated for the three gases from the SOCW model and the values resulting from the other two recently ublished models valid along the saturation line of water [17,63]. It is aarent that the agreement among the models at sat w is quantitative for CH 4 and CO 2. Some differences are observed for H 2 S due to higher uncertainty in the Henry s law constants that are not quite consistent at elevated temeratures with the C, and V s data. Figs. 1 4 illustrate the changes in the Henry s law constant with the structure of the solute and with temerature and ressure u to 623 K and 80 MPa for rocarbons having eight carbon atoms and for the three gases. First the results of the calculation for K H from

7 V. Majer et al. / Fluid Phase Equilibria able 5 Henry s law constants calculated along the saturation line of water and at elevated ressures from the resented model for octane, methane, carbon dioxide and rogen sulfide MPa ln K H at 298 K ln K H at 373 K ln K H at 473 K ln K H at 573 K n-octane sat CH 4 sat Ref. [17] at sat Ref. [63] at sat Fig. 1. he Henry s law constants calculated along the saturation line of water from the grou contribution model [15] for C 8 rocarbons: n-octane full, 1-octene long-dashed, ethylcyclohexane short-dashed and ethylbenzene dashed-dot line. CO 2 sat Ref. [17] at sat Ref. [63] at sat H 2S sat Ref. [17] at sat Ref. [63] at sat Comarison for CH 4,CO 2 and H 2Sat sat with the values in italics calculated from the formulations of Fernandez-Prini et al. [17] and of Akinfiev and Diamond [63]. Fig. 2. he Henry s law constants for n-octane calculated as a function of temerature along the saturation line of water full and at ressures of 40 MPa long-dashed and 80 MPa short-dashed line. the grou contributions are resented along the saturation line of water for four different C 8 rocarbons Fig. 1 and for n-octane as a function of temerature and ressure Fig. 2. Second, analogous lots are in Figs. 3 and 4 for the aqueous gases. able 6 listing the ratios K H /K H sat w for octane, methane, carbon dioxide and rogen sulfide at three ressures and four temeratures summarizes quantitatively the change of the Henry s law constant with ressure for the four solutes. It is aarent from Eq. 9 that the standard molar volume of a solute lays a major role in determining this factor. hus, the ressure effect is much stronger for octane than for the three gaseous solutes due to Fig. 3. he Henry s law constants calculated along the saturation line of water from the resented model for methane full, carbon dioxide long-dashed and rogen sulfide short-dashed line. Fig. 4. he Henry s law constants for carbon dioxide calculated as a function of temerature along the saturation line of water full and at ressures of 40 MPa long-dashed and 80 MPa short-dashed line.

8 72 V. Majer et al. / Fluid Phase Equilibria able 6 Ratios K H/K H sat w for octane, methane, carbon dioxide and rogen sulfide K H/K H sat w 323 K sat w 0.1MPa 373Ksat w 0.1MPa 473Ksat w 1.6MPa 573Ksat w 8.7MPa 10 MPa 50 MPa 100 MPa 10 MPa 50 MPa 100 MPa 10 MPa 50 MPa 100 MPa 10 MPa 50 MPa 100 MPa Octane CH CO H 2S the difference in the V s values about 100 cm3 /mol for C 8 H 18 and close to 35 cm 3 /mol for the three gases at K. At suerambient conditions, the standard molar volume increases substantially with increasing temerature and decreases with ressure, it scales aroximately with the comressibility of water and diverges at the critical oint of the solvent. For the ressures deendence of K H the increase in volume at high temeratures is, however, artly comensated by dividing with temerature in Eq. 9. herefore, the relative ressure effect on K H does not change much with temerature at conditions remote from the critical oint of water. 4. Software ackage for calculating the Henry s law constant and related distribution coefficients As aarent from the equations listed in Aendix A, the alied model is rather comlex and requires the use of a fundamental equation of state allowing calculation of the thermodynamic roerties of water. A rogramming effort would be necessary before using the method. In addition, the Henry s law constant or another related coefficients are required in varying ressure and concentration units deending on the users and erroneous conversions often lead to confusion. For that reason we have reared a comuter code with a user-friendly interface allowing generation of the Henry s law constants from the model as a function of temerature and ressure in several tyes of units as well as the calculation of other two coefficients defined by Eqs. 13 and 16 that are closely related to the Henry s law constant. Using the grou contributions listed in ables 1 and 2 the estimations can be erformed for normal and branched alkanes and alkenes C 2 to C 12 and for the monocyclic saturated or aromatic rocarbons tyically for C 6 ring comounds with one or several alkyl grous u to C 8. In addition, the software uses secific arameters for methane, carbon dioxide and rogen sulfide. he calculations can be made at temeratures u to 623 K either along the saturation line of water or at distinct airs of temerature and ressure sat w <<100 MPa. When running the rogram the user chooses from several otions allowing the calculation of one of the following arameters: the Henry s law constant K H defined in terms of the mol fraction Eq. 1, its modifications K Hm and K Hc Eq. 6 using as concentration variables molality mol/kg or molarity mol/m 3, resectively, the air water artition coefficient K aw Eq. 16 and the vaor liquid distribution constant relative volatility K d Eq. 13. he air water artition coefficient is used for exressing the artition of a solute between air and water at near-ambient conditions and the calculation is made therefore only at ressures below 0.5 MPa. Similarly due to its definition the vaor liquid distribution constant can be calculated solely along the saturation line of water. he five coefficients are in the code interconnected by the limiting conversion exressions as follows K H = K Hm = K Hc w = K awr w = K d 29 m o M w c o M w M w sat,w where the meaning of individual symbols was exlained above see Eqs. 6, 14 and 17. Comared to Eq. 14 it is aarent that the saturation ressure of water is used in the conversion Eq. 29 instead of fugacity. his simlifying assumtion of an ideal gas behavior of the vaor hase can lead to an increase of uncertainty in K d at high temeratures where the fugacity coefficient of water can differ significantly from unity. he code is available on request as shareware for noncommercial users from academia contacts: vladimir.majer@univbclermont.fr and josef.sedlbauer@tul.cz. he rearation of inut files, the oeration of the code and a few illustrative examles of the inut and outut files are described in the README document that is distributed along with the software. List of symbols c molarity C heat caacity f fugacity G Gibbs energy H enthaly K aw air water artition coefficient K d vaor liquid distribution coefficient K H Henry s law constant m molality M molar mass N total number of functional grous in a molecule O minimized objective function ressure R universal gas constant S entroy SS intrinsic value thermodynamic temerature V volume x molar fraction liquid hase X artial molar roerty X = G, H, S, V, C y molar fraction gaseous hase Greek letters exansivity activity coefficient change ϕ fugacity coefficient comressibility density absolute error Suerscrits a air hase calc calculated cor correction term ex exerimental g gas hase H roerty comatible with the Henry s law ig ideal gas l liquid hase mod high-temerature model R roerty comatible with the Raoult s law sat saturation sol solubility

9 w aqueous hase standard state of infinite dilution limiting value ure comound Subscrits c relating to molarity ration m relating to molality o unit value ref reference state s solute sol dissolution SS intrinsic value w water x relating to molar fraction Acknowledgements he authors thank Roberto Fernandez-Prini and Jorge L. Alvarez for roviding the direct values of the Henry s law constant for CH 4, CO 2 and H 2 S used for establishing arameters of the correlations ublished in ref. [17]. J.S. acknowledges the suort by the Research Centre Advanced Remediation echnologies and Processes. V. Majer et al. / Fluid Phase Equilibria ıex[ w ] 1 c ex [ ] +Rc ex [ ] 2 w 3 2 w +R ϑb ex[ϑ w ] + ı ex[ w ] [ ] 2 w + R 2 a + bex[ϑ w ] 1 + c ex +ıex[ w ] 1 + C cor A.4, where G w, H w, C,w are the molar Gibbs energy, enthaly and heat caacity of water, Gw,H ig w,c ig ig,w are the same roerties of water in an ideal gas standard state and w = 1/ w w / is the isobaric coefficient of thermal exansion. hermodynamic roerties of water were obtained in this study from the equation of state by Hill [64]. he correction terms are exressed by an emirical function with one additional adjustable arameter, e C cor, = e c 2 S cor = e c [ c 2 ] ln + c 2 ln c A.5 [ ] A.6 c Aendix A. hermodynamic functions of ration from the SOCW model he Gibbs energy of ration is exressed in the SOCW model [16] as: [ G = R ln w ] [ R + d G w G ig w ] R w R ln M w ref M w ref [ ] +R w a + c ex b ı + b ϑ ex[ϑ w] 1 + ı ex[ w] 1 + G cor A.1 Aroriate temerature derivations of G see Eqs. 3, 7 and 8 in the main text lead to other thermodynamic roerties of ration H = R w 1 + dh w H ig w R w 1 [ ] w +Rc ex R 2 w a + bex[ϑ w ] 1 [ ] +c ex + ıex[ w ] 1 + H cor A.2 H S = G C, = 2R w + R 2 w R + d C,w C ig,w 2R w + R 2 w R A.3 [ ] w 2R a + bex[ϑ w ] 1 + c ex H 2 cor = e c c c 2 [ + c 2 ] ln c A.7 G cor = H cor S cor A.8 where = 228 K is a general constant. Correction terms defined by Eqs. A.5 A.8 aly only at temeratures below the critical temerature of water c = K and are by definition equal to zero at c 0. All thermodynamic roerties that aear in the above equations should be alied in their basic SI units when using arameters from able 2 of the main text. References [1] W. Henry, R. Soc. London Philos. rans , [2] J. Hine, P.K. Mookerjee, J. Org. Chem [3] W.M. Meylan, P.H. Howard, Environ. oxicol. Chem [4] N. Nirmalakhandan, R.E. Seece, Environ. Sci. echnol [5] N. Nirmalakhandan, R.A. Brennan, R.E. Seece, Water Res [6] M.H. Abraham, J. Andonian-Haftvan, G.S. Whithing, A. Leo, S. aft, J. Chem. Soc. Perkin rans [7] S.R. Sherman, D.B. rame, D.M. Bush, M. Schiller, C.A. Eckert, A.J. Dallas, J. Li, P.W. Carr, Ind. Eng. Chem. Res [8] K.-U. Goss, Fluid Phase Equilib [9] S.-. Lin, S.I. Sandler, Chem. Eng. Sci [10] E.J. Delgado, J. Alderete, J. Chem. Inf. Comut. Sci [11] E.J. Delgado, J. Alderete, J. Chem. Inf. Comut. Sci [12] N.J. English, D.G. Carroll, J. Chem. Inf. Comut. Data [13] X. Yao, M. Liu, X. Zhang, Z. Hu, B. Fan, Anal. Chem. Acta [14] D. Yaffe, Y. Cohen, G. Esinosa, A. Arenas, F. Giralt, J. Chem. Inf. Comut. Sci [15] J. Sedlbauer, G. Bergin, V. Majer, AIChE J [16] J. Sedlbauer, J.P. O Connell, R.H. Wood, Chem. Geol [17] R. Fernandez-Prini, J.L. Alvarez, A.H. Harvey, J. Phys. Chem. Ref. Data [18] S.I. Sandler, Chemical Engineering hermodynamics, third ed., Wiley, New York, [19] J.M. Prausnitz, R.N. Lichtenthaler, E.G. de Azevedo, Molecular hermodynamics of Fluid Phase Equilibria, third ed., Prentice Hall, New Jersey, [20] M.A. Anisimov, J.V. Sengers, J.H.M. Levelt Sengers, in: D.A. Palmer, R. Fernandez- Prini, A.H. Harvey Eds., Aqueous Systems at Elevated emeratures and Pressures, Elsevier, Oxford, 2004, [21] J.J. Carroll, F.-Y. Jou, A.E. Mather, Fluid Phase Equilib [22] J.J. Carroll, A.E. Mather, Chem. Eng. Sci [23] F.-Y. Jou, A.E. Mather, J. Chem. Eng. Data

10 74 V. Majer et al. / Fluid Phase Equilibria [24] V. Majer, J. Sedlbauer, R.H. Wood, in: D.A. Palmer, R. Fernandez-Prini, A.H. Harvey Eds., Aqueous Systems at Elevated emeratures and Pressures, Elsevier, Oxford, 2004, [25] A.V. Plyasunov, E.L. Shock, Geochim. Cosmochim. Acta [26] A.V. Plyasunov, J.P. O Connell, R.H. Wood, E.L. Shock, Geochim. Cosmochim. Acta [27] A. Ben-Naim, Solvation hermodynamics, Plenum Press, New York, [28] A. Michels, J. Gerver, A. Bijl, Physica [29] O.L. Culberson, J.J. McKetta, AIME Petrol. rans [30] R.G. Sultanov, V.G. Skrika, A.Yu. Namiot, Gazov. Prom [31].R. Rettich, Y.P. Handa, R. Battino, E. Wilhelm, J. Phys. Chem [32] S.D. Cramer, Bureau of Mines Reort of Investigations 8706, U.S. Det. of the Interior, [33] R. Crovetto, R. Fernandez-Prini, M.L. Jaas, J. Chem. Phys [34] S.F. Dec, S.J. Gill, J. Sol. Chem [35] S.F. Dec, S.J. Gill, J. Sol. Chem [36] G. Oloffson, A.A. Oshodj, E. Qvarnstrom, I. Wadsö, J. Chem. hermodyn [37] H. Naghibi, S.F. Dec, S.J. Gill, J. Phys. Chem [38] L. Hnedkovsky, R.H. Wood, J. Chem. hermodyn [39] E.W. ieel, K.E. Gubbins, J. Phys. Chem [40] M.W. Chase Ed., NIS-JANAF hermochemical ables, fourth ed., J. Phys. Chem. Ref. Data Monograh No. 9, New York, [41] J.C. Moore, R. Battino,.R. Rettich, Y.P. Handa, E. Wilhelm, J. Chem. Eng. Data [42] L. Hnedkovsky, R.H. Wood, V. Majer, J. Chem. hermodyn [43] R. Wiebe, V.L. Gaddy, J. Am. Chem. Soc [44] R. Wiebe, V.L. Gaddy, J. Am. Chem. Soc [45].J. Morrison, F. Billet, J. Chem. Soc [46] S.D. Malinin, Geokhimia [47] A.J. Ellis, R.M. Golding, Am. J. Sci [48] S. akenouchi, G.C. Kennedy, Am. J. Sci [49] C.N. Murray, J.P. Riley, Dee-Sea Res [50] R.A. Shagiakhmetov, A.A. arzimanov, in: P. Scharlin Ed., IUPAC Solubility Data Series, 62, Oxford University Press, Oxford, 1996,. 60. [51] G. Müller, E. Bender, G. Maurer, Ber. Bunsenges. Phys. Chem [52] J.A. Nighswander, N. Kalogerakis, A.K. Mehrotra, J. Chem. Eng. Data [53] R. Crovetto, R.H. Wood, Fluid Phase Equilib [54] A. Bamberger, G. Sieder, G. Maurer, J. Suercrit. Fluids [55] R.L. Berg, C.E. Vanderzee, J. Chem. hermodyn [56] J.A. Barbero, L.G. Heler, K.G. McCurdy, P.R. remaine, Can. J. Chem [57] F.. Selleck, L.. Carmichael, B.H. Sage, Ind. Eng. Chem [58] J.I. Lee, A.E. Mather, Ber. Bunsenges. Phys. Chem [59] P.C. Gillesie, G.P. Wilson, GPA Research Reort RR-48, Gas Processors Association, ulsa, [60] J.J. Carroll, A.E. Mather, Geochim. Cosmochim. Acta [61] J.D. Cox, D.D. Wagman, V.A. Medvedev, CODAA Key Values for hermodynamics, Hemishere Publishing Cor, [62] J.A. Barbero, K.G. McCurdy, P.R. remaine, Can. J. Chem [63] N.N. Akinfiev, L.W. Diamond, Geochim. Cosmochim. Acta [64] P.G. Hill, J. Phys. Chem. Ref. Data [65] J. Alvarez, R. Fernández-Prini, J. Sol. Chem